I have purchased a Roamio Pro and a Mini.
The Roamio will be in the living room and the Mini in the study area. I have a wi-fi set up in the study.
Does everything I need to get set up and going come pre-packaged in the Roamio and Mini? Stated another way-- will I need to buy anything else?

For previous Tivo set-up I needed to purchase a wireless adapter.

Will I need any MOCA adapter?
I am aware that I will need one cable card (from Comcast).

I do not plan to use any ethernet cable or other cables from the router to either the Roamio or Mini.

As stated in many places on the internet, wi-fi will not cut it for streaming from the Roamio to the Mini. You will need to use either ethernet or MOCA. You will not need to provide a MOCA adapter as both devices will have the gear needed to implement MOCA from the Roamio to the Mini. This means the Mini must have the Coax connector wired to your cable. You should also put a POE filter where cable enters the house.

You can use the built in WiFi adapter in the ROAMIO in order for the TiVos to reach the internet, both for streaming shows from the internet and downloading guide data.

Same here, I have two Minis use wireless N bridges sucessfully - but that doensn't mean that it will work for everybody else. Wireless networks may fluctuate in speed greatly based on your local conditions and the hardware you are using - those fluctuations you may not even notice when using a computer for the usual tasks like web browsing and email but they can certainly kill the user experience when playing back HD recordings.